Pre-Algebra Examples

$2 {(x + 5)}^{2} = 72$

Step 1

Divide each term in $2 {(x + 5)}^{2} = 72$ by $2$ and simplify.

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Step 1.1

Divide each term in $2 {(x + 5)}^{2} = 72$ by $2$ .

$\frac{2 {(x + 5)}^{2}}{2} = \frac{72}{2}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $2$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{2 {(x + 5)}^{2}}{2} = \frac{72}{2}$

Step 1.2.1.2

Divide ${(x + 5)}^{2}$ by $1$ .

${(x + 5)}^{2} = \frac{72}{2}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $72$ by $2$ .

${(x + 5)}^{2} = 36$

Step 2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x + 5 = \pm \sqrt{36}$

Step 3

Simplify $\pm \sqrt{36}$ .

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Step 3.1

Rewrite $36$ as $6^{2}$ .

$x + 5 = \pm \sqrt{6^{2}}$

Step 3.2

Pull terms out from under the radical, assuming positive real numbers.

$x + 5 = \pm 6$

Step 4

The complete solution is the result of both the positive and negative portions of the solution.

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Step 4.1

First, use the positive value of the $\pm$ to find the first solution.

$x + 5 = 6$

Step 4.2

Move all terms not containing $x$ to the right side of the equation.

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Step 4.2.1

Subtract $5$ from both sides of the equation.

$x = 6 - 5$

Step 4.2.2

Subtract $5$ from $6$ .

$x = 1$

Step 4.3

Next, use the negative value of the $\pm$ to find the second solution.

$x + 5 = - 6$

Step 4.4

Move all terms not containing $x$ to the right side of the equation.

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Step 4.4.1

Subtract $5$ from both sides of the equation.

$x = - 6 - 5$

Step 4.4.2

Subtract $5$ from $- 6$ .

$x = - 11$

Step 4.5

The complete solution is the result of both the positive and negative portions of the solution.

$x = 1, - 11$